Echoing what the others have suggested, I would also add, especially for you smaller garden, to cover the entire garden with a layer of heavy black plastic. We've used it for several years here in the U.S. and while not 100% effective in controlling early weed germination it does help significantly. Just layer it over the garden and hold the edges down with rocks, boards or other material to keep the wind from moving it.
An additional benefit is that the soil reaches the minimum temperature for plants and seed germination (about 50 degrees (F) here)much earlier.
When removed in the spring, we fold it and save it for the next year. It's inexpensive and you might Google "soil solarization" to see the discussions about clear vs. black plastic as well as other methods of achieving better control of weeds...